Cross Validated Asked on January 3, 2022
From the Quarterly Workforce Indicators, I have obtained a measure of data measured at the quarterly level for earnings and employment.
so in each quarter, they take the total earnings, and divide by the total employment for that quarter. I want to create an ‘implied’ annual average earnings from this. A few questions:
would it be invalid to just take the average of the average quarterly earnings, and multiply that by 4?
alternatively, since I can obtain the denominator for each quarter, I wished to do the following:
for each quarter q, multiply average quarterly earnings by the total employment in that quarter. this should yield the total quarterly earnings.
Do this for each quarter, and then add each to get the total annual earnings. divide by the total annual employment.
is 2. equivalent to a ‘weighted’ mean? or can it be directly interpreted as an annual average earnings? my concern is that since each measurement is calculated independently each quarter, the denominator and the numerator could be double counting many jobs.
Answer to Q1: While imperfect, that approach is preferable out of the two you've presented here. Your 'implied' annual average will generally be higher than the actual annual average, with the extent of this error rising with employment churn. Consider calling the result the "quarterly earnings per employment, averaged for the year" or similar, so that your figure isn't misconstrued as annual earnings per employment. Or, if you have the time and inclination, you could report something more sophisticated than a ratio; consider an Autocorrelated Error Model, e.g. Chapter 16 of Griffiths et al, below.
Answer to Q2: This is often done when the data points are independent; the established techniques of “ratio estimation” are covered in, for example, Section 7.4 of John Rice’s textbook (below). However, your data aren't independent. You have four highly dependent readings of a two-dimensional signal (one dimension is earnings, one is employment). You’re quite right to be concerned about what you call double counting, for this particular problem.
Good luck!
References:
Answered by Mark Ebden on January 3, 2022
1 Asked on December 20, 2021
1 Asked on December 20, 2021 by 24n8
2 Asked on December 20, 2021 by dionysis-m
0 Asked on December 20, 2021 by frass
generative models logistic machine learning references sampling
0 Asked on December 20, 2021 by terauser
biostatistics measurement error multivariate analysis rda statistical significance
0 Asked on December 20, 2021
1 Asked on December 20, 2021 by dynamic89
1 Asked on December 20, 2021
bayesian hierarchical bayesian normalization probability simulation
1 Asked on December 20, 2021 by eurohacker
0 Asked on December 20, 2021
1 Asked on December 18, 2021 by kellyyang
categorical data multicollinearity variance inflation factor
3 Asked on December 18, 2021 by mehraban
2 Asked on December 18, 2021 by zhubarb
1 Asked on December 18, 2021 by denby47
inference likelihood mathematical statistics maximum likelihood profile likelihood
2 Asked on December 18, 2021
1 Asked on December 18, 2021 by bayesisbaye
3 Asked on December 18, 2021 by floyd
1 Asked on December 18, 2021 by xorion-1997
moment generating function multivariate normal distribution probability quadratic form self study
0 Asked on December 18, 2021 by ian-lane
distance multivariate analysis partial correlation permutation test spatial
Get help from others!
Recent Questions
Recent Answers
© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP